I was going to say trotzdem means something more like despite that... rather than just however but if we had a context along the lines of "He gave us the key to open the door. Despite that, it is not possible" then it might be translated as "Er gab uns den Schlüssel, um die Tür zu öffnen. Trotzdem ist es nicht möglich." So trotzdem seems like it could work. But then I'm a beginner here too so I'll be curious to hear what is said!